Browser safe color problem

I'm confused. Using the broswer safe palette I made a graphic which
converted to GIF just fine. Then I reduced the original (PhotoShop 4) and
converted to GIF again only this time the colors are no longer browser safe
(I get those irritating little dots in the colors).

In both instances when converting to GIF I choose Adaptive, 7 bit (for
size), but it seems like no matter what I try it still happens. 

The first color, for example, starts out as RGB 0:153:255 and ends up as
0:156:255. You can see the nightmare here:
http://www.mindspring.com/~martinb/dv_test.htm

How do I keep these colors from changing? (I don't even care why it does it
on the small ones, but not the large ones, unless that matters.)

There are only 5 colors (all browser safe) in the image. I assume there is
something I can do in the convert process, but what?
---
Martin Blackwell
martinb(at)mindspring.com

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